Poor old Gordon Brown. His joy at being given a World Statesman of the Year award must have been severely tempered by having to deny he's been snubbed by Barack Obama and upstaged by Muammar Gaddafi on the same day.

All that and denying he's about to resign because he's losing his sight. Thank goodness he's so resilient and will easily shake it off. Not.

All the same, you would have thought that Libya's Colonel Gaddafi would be sufficiently in touch with reality to remember not to bomb the prime minister's speaking slot at the UN general assembly.

After all, the pair have been through a lot together this summer during the row over Scotland's release of the convicted Lockerbie bomber.

Never mind. Contrary to misleading appearances most gigs at the UN, an important but awful place, are a bit like getting a spot at the Labour party conference. It looks better than it actually is and probably fails even to impress cynical domestic audiences who are obliged to watch the whole thing on Tyrant TV stations around the world.

Such neurosis. After all, Obama has been pretty busy at the UN and has seen and heard quite a lot of Fife's finest in recent months and will do so again at the G20 in Pittsburgh. Other people need face time too, and China is even bigger, even more important, than Britain these days, so some geographers claim.

Never forget too that Obama was born in Hawaii, not Maine (or even Kenya): he's a child of the Pacific. It's not as if the wimpy Europeans have impressed him much since taking office – not much help on Afghanistan or taking some of those Guantánamo prisoners they're so keen he release. Not great on economic recovery either.

Brown is different, of course. He loves America and what it stands for. He's done his best across a range of policies too, though obviously he blotted his copybook over the Megrahi release, even though the deed was actually done by his old foe, First McMinister Alex Salmond. Americans don't do nuance much where foreign forms of government are concerned.

All the same, from this distance I doubt if the snub was a direct consequence of the Gaddafi row, though one can never be sure.

Margaret Thatcher was said to have been snubbed by Jimmy Carter before she beat Carter's chum Jim Callaghan in 1979, though Callaghan actually preferred dealing with the very steady Republican, Gerald Ford, whom Carter beat in 1976.

And Michael Howard was certainly put in the White House freezer by the Bushies after wriggling over Tory support for the 2003 Iraq war, which Tony Blair joined with – at the time – Conservative backing.

I have some direct experience of this sort of tiff. I rang Howard's spokesman when I read his wriggle in the Sunday Times, reluctant to believe that such a smart man had been so foolish. Had he been misquoted? No, Mike, what's your problem with it? Not my problem, chum, your problem.

But as the Guardian's US correspondent in the mid-80s I was also present during Neil Kinnock's unhappy visit to Washington and New York in 1987 when he was a Labour leader seeking to show he was a global player – despite being poised to fight a general election on a policy of expelling US nuclear bases from Britain.

Even Democrats were offended by that policy, which Kinnock abandoned by the 1992 election, as foolish in its way as Howard's wriggle – although more forgivable given Labour's lumpen sentiments in those pre-Blair days.

But the Kinnock trip and the short interview that Reagan gave him and Denis Healey (whom the president mistook for bushy-eyebrowed Oliver Wright, our ambassador, who died the other day) was turned into a major storm – "Snub to Kinnock" etc etc – by the visiting press pack. In reality it was a real, but modest, one.

I smelled a rat when Kinnock addressed a business meeting in New York and was asked a very detailed question about a dubious policy proposal by Michael Meacher, then as now a slightly off-piste Labour leftwinger with a wacky sense of political timing.

How could this New Yorker know the mind of the sage of Oldham without a bit of help, I wondered. I still do. I wonder too about the questions Brown was asked on BBC Five Live and on NBC in the US about his health. He was forced to deny that's he losing the sight in his remaining good eye. But it allowed the papers to print the rumours at last.

That's part of the political cycle too. Prime ministers on their way out – Blair, Major, Thatcher, Wilson, Heath (not Callaghan) – were variously accused of being mad, ill or drunk in their declining years. It happens, and there was sometimes a kernel of truth to the charges.

There have been rumours around the Westminster village for weeks that Brown is on one kind of medication or another, that he's depressed, that he's going to step down, as Charles Clarke counterproductively urged him to do again yesterday. There was no evidence to justify reporting it beyond the wilder shores of blogging – until yesterday from New York.

But Sky TV's political editor, Adam Boulton (married to the Blairite princess Anji Hunter), gave the rumours a leg up in the new paperback edition of his memoirs, serialised by the class enemy, the Mail on Sunday. Tony Blair believes Brown is "a quitter, not a fighter" like Peter Mandelson has proved to be, Boulton reported.

True or not? I don't know. Blair no longer talks to the rough trade and has been admirably discreet towards Brown. Though I remain pretty confident GB will not quit, as gossip it sounds plausible. We just don't know.

The trouble is with Brown, as it is with most British leaders, is that he invests too much in the special relationship with the US, far more than Washington does, deep and real though the ties that bind us are (says me).

Brown is just a bit more neurotic, a bit more desperate for a sprinkling of Obama stardust than the average British PM. But he has less to offer than, say, a Blair or Thatcher, both upbeat characters who made themselves genuinely famous in America. Being Eeyore doesn't work there as it does at a Lib Dem conference.

Being a British PM in America must be a bit like being the oldest wife of a wealthy Muslim. You've been around a long time. You know that hubby is interested in other, younger girls: they're prettier, they make him feel good, some of them have got bigger GDPs. They flatter his possibly flagging powers, and, hey, they're new.

Do you get upset when he takes another wife? Or do you take the long view and make yourself obliging to the younger wives, promoting the interests of the smarter ones who will bear your interests in mind too. Don't be a bore, don't whinge and he'll probably start dropping by for a chat and a cup of mint tea pretty often. After all, you're old friends ...

No, I don't see Gordon seeing it that way either. Look what a pointless fuss was made (by No 10 or the British press?) of the modest DVD set Obama gave Brown on an earlier visit.

A US diplomat told me at the time that their advice to No 10 was to tell the press how much Gordon and Sarah enjoyed the DVDs and move on. That's the spirit. What with the global economy and climate change Brown has much more important things to worry about.

The odd thing is, he knows this. It's the little things that seem to cause so much grief.